Article

Nonlocal Inverse Problem for Determining the Unknown Coefficient in the Beam Vibration Equation

D. K. DurdievBukhara Branch of Romanovskii Institute of Mathematics, Uzbekistan Academy of Sciences, Bukhara, 200117, UzbekistanZavqiddin BozorovBukhara Branch of Romanovskii Institute of Mathematics, Uzbekistan Academy of Sciences, Bukhara, 200117, Uzbekistan

Journal of Applied and Industrial Mathematicsjournal2023en

ABI

Abstract

The paper is devoted to the study of the direct problem for the vibration of a homogeneous beam of finite length with nonlocal time conditions. Necessary and sufficient conditions for the existence of a solution of the direct problem are obtained. For the direct problem, we study the inverse problem of determining the time-dependent coefficient multiplying a lower-order derivative. Using the eigenvalues and eigenfunctions, the problem is reduced to a system of integral equations. The existence and uniqueness of the solution of inverse problems are shown using the Banach principle.

Topics

Numerical methods in inverse problems Differential Equations and Boundary Problems Elasticity and Wave Propagation

Identifiers

DOI: 10.1134/s1990478923020060

Citations and references

Cited by 1 25 references

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